Robust flexible adaptation gain based CRM for guaranteed transient performance

Abstract

High adaptation gain in model reference adaptive control (MRAC) with closed-loop reference models (CRMs) is a necessary requirement to ensure guaranteed transient performance with better tracking and fast convergence. The high adaptation gain, however, may excite unmodelled dynamics, leading to instability, making the differential equations of the adaptive law stiff and causing numerical instability. Therefore, it becomes apparent that a compromise is required on either convergence speed and transient performance or system stability. This paper attempts to address these issues with a novel CRM-MRAC architecture with flexible adaptation gain, which varies as a function of the derived parameter estimation error. The proposed adaptive scheme mathematically ensures a designable upper bound of the L ∞ norm; it also ensures the absence of high-frequency oscillations in the control input, thereby making the system more robust and stable. The effectiveness of the proposed work has been validated with simulation studies on a standard numerical example and the performance has been compared with recent similar works.

An improved 2-level MPPT scheme for photovoltaic systems using a novel high-frequency learning based adjustable gain-MRAC controller

“…Since, from 16 , 20 , 24 , the inequality follows holds therefore, the results in ( 28 ) immediately follows. Similarly, …”

“…The control signal of the controller must not have high-frequency oscillations. These high-frequency oscillations may cause numerical instability and make the adaptive law stiff, which in turn may leads system to instability 15 , 16 , 20 .

Figure 15 Comparison of control signals .

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“…The proof of theorem 1 can be obtained in a similar way as in 20 , 21 . For the proof the Lyapunov function can be considered as where are symmetric positive definite static gains, and is positive definite high-pass filter gain matrix and its filtered error dynamics is given by where is the resultant output of the high-pass filter, in s-domain it is given as, where is the time constant of the low-pass filter, and its optimum value is found using genetic algorithm 19 .…”

“…The low-pass filtered parameter estimation error satisfies 20 , where , represents the respective positive upper bounds.…”

Comparação Entre Técnicas de Busca Meta-Heurísticas para a Otimização de um MRAC

“…Nounou and Passino (2000) emprega uma estrutura de auto-tuning para isso, de forma que os valores destes ganhos variem de acordo com uma lei de sintonia que garante a estabilidade do sistema. Já Dey et al (2018) propõe outro tipo de sistema com ganhos de adaptação variáveis, no qual o sinal usado para se determinar tais ganhosé o erro de estimação dos parâmetros de controle. Tal método garante a robustez da performance do controle mesmo com a presença de incertezas.…”